Thermodynamics of AdS/QCD

We study finite temperature properties of four dimensional QCD-like gauge theories in the gauge theory/gravity duality picture. The gravity dual contains two deformed 5d AdS metrics, with and without a black hole, and a dilaton. We study the thermodynamics of the 4d boundary theory and constrain the two metrics so that they correspond to a high and a low temperature phase separated by a first order phase transition. The equation of state has the standard form for the pressure of a strongly coupled fluid modified by a vacuum energy, a bag constant. We determine the parameters of the deformation by using QCD results for $T_c$ and the hadron spectrum. With these parameters, we show that the phase transition in the 4d boundary theory and the 5d bulk Hawking-Page transition agree. We probe the dynamics of the two phases by computing the quark-antiquark free energy in them and confirm that the transition corresponds to confinement-deconfinement transition.Comment: 1+19 pages, 6 figures, references added, section 3 improve

Classical limit of quantum gravity in an accelerating universe

A one-parameter deformation of Einstein?Hilbert gravity with an inverse Riemann curvature term is derived as the classical limit of quantum gravity compatible with an accelerating universe. This result is based on the investigation of semi-classical theories with sectional curvature bounds which are shown not to admit static spherically symmetric black holes if otherwise of phenomenological interest. We discuss the impact on the canonical quantization of gravity, and observe that worldsheet string theory is not affected.Comment: 11 pages, no figure

Energy-Momentum Restrictions on the Creation of Gott Time Machines

The discovery by Gott of a remarkably simple spacetime with closed timelike curves (CTC's) provides a tool for investigating how the creation of time machines is prevented in classical general relativity. The Gott spacetime contains two infinitely long, parallel cosmic strings, which can equivalently be viewed as point masses in (2+1)-dimensional gravity. We examine the possibility of building such a time machine in an open universe. Specifically, we consider initial data specified on an edgeless, noncompact, spacelike hypersurface, for which the total momentum is timelike (i.e., not the momentum of a Gott spacetime). In contrast to the case of a closed universe (in which Gott pairs, although not CTC's, can be produced from the decay of stationary particles), we find that there is never enough energy for a Gott-like time machine to evolve from the specified data; it is impossible to accelerate two particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism different from that which operates in a closed universe. In proving our result, we develop a simple method to understand the inequalities that restrict the result of combining momenta in (2+1)-dimensional gravity.Comment: Plain TeX, 41 pages incl. 9 figures. MIT-CTP #225

Structural Scaling Metrics For Tensioned-Blanket Space Systems

Structural metrics have been used for nearly a century to provide designers with simple, rational tools for comparing the mass performance of aircraft and spacecraft platforms. Large space structures designers and evaluators rely on metrics to compare boom, telescope, and long antenna architectures. In this work, scaling metrics are established for rectangular flexible blanket solar array structural architectures. The approach takes advantage of the fact that an ideal solar array structure is a system of coupled beam and tensioned blanket components rather than the typical simplifying approach of considering only one beam with a distributed mass as the blanket. A fundamental frequency relation is developed to represent a beam-cable system in a clamped-free boundary condition. A structural model of the array is developed on the basis of minimum mass and minimum beam cost using constraint analysis methods and weight equations. This structural model expression is solved numerically using root finding algorithms, is transformed into an approximate expression using regression techniques, and the terms are symbolically related into scaling parameters and scaling indices. These metrics enable straightforward comparison of a wide range of array sizes, geometric forms, column types, column quantities, blanket mass densities, acceleration loads, fundamental frequencies, and power production values. Finally, practical application and accuracy of these metrics is demonstrated by comparing to the latest heritage tensioned blanket systems on-orbit and those still in prototype form: Terra (EOS-AM), the Milstar constellation, the International Space Station, MegaROSA, and MegaFlex

Variational methods, multisymplectic geometry and continuum mechanics

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic reduction and for the further development of Veselov-type multisymplectic discretizations and numerical algorithms. The latter will be the subject of a companion paper